How to add a mouse-over summary

I don't see why your first attempt wouldn't work. It's the <summary> comment tag which supplies the 'tooltip' you're talking about...

/// <summary>
/// This text should automatically show up as the summary when hovering over
/// an instance of this class in VS
/// </summary>
public class MyClass
{
    public MyClass() {}      
}

public class MyClass2
{
    public MyClass()
    {
        //hovering over 'something' below in VS should provide the summary tooltip...
        MyClass something = new MyClass();
    }
}

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Two additions to check for that I just discovered will prevent the summary from showing when hovering:

Do not use ampersands (&) or starting angle brackets (<) in your summary description.

Breaks:

    ///<summary>
    ///Class does this & that
    ///</summary>

Instead use:

    ///<summary>
    ///Class does this AND that
    ///</summary>

Breaks:

    /// <summary>
    /// Checks if this < that
    /// </summary>

This will work, but probably not a good precedent to set:

    /// <summary>
    /// Checks if this > that 
    /// </summary>

---

Do not separate the /// lines from each other.

Breaks:

    /// <summary>
    /// This text will not show
    
    /// </summary>

Breaks:

    /// <summary>
    /// This text will also not show
    //  because THIS line only has 2 dashes
    /// </summary>

Works:

    /// <summary>
    ///
    /// This
    ///    
    /// is
    ///
    /// fine.
    ///
    /// </summary>

The three-slash XML comments may be used to create the IDE tool-tips in Visual Studio. In particular, "summary" and "exception" work very well. (Other things like "code" have not worked in the versions of Visual Studio that I have used.)

If this is not working for you, then something may be wrong with your settings.